scholarly journals SPACE-TIME FROM THE SPECTRAL POINT OF VIEW

2012 ◽  
Author(s):  
ALI H. CHAMSEDDINE ◽  
ALAIN CONNES
Keyword(s):  
Space Time ◽  
Point Of View ◽  
Spectral Point

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

scholarly journals A TORSIONAL TOPOLOGICAL INVARIANT

2007 ◽  
Vol 22 (29) ◽  
pp. 5237-5244 ◽  
Author(s):  
H. T. NIEH
Keyword(s):  
Affine Connection ◽  
Euler Class ◽  
Christoffel Symbol ◽  
Space Time ◽  
Topological Invariant ◽  
Point Of View ◽  
Underlying Space ◽  
Recent Developments ◽  
Theory Point ◽  
Curvature And Torsion

Curvature and torsion are the two tensors characterizing a general Riemannian space–time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space–time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space–time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

The Tale of Fabled Creatures

2021 ◽  
pp. 215-233
Author(s):  
M. Nur Erdem
Keyword(s):  
Digital Media ◽  
Daily Life ◽  
Space Time ◽  
Point Of View ◽  
The Other ◽  
Other Hand ◽  
The Media ◽  
The Subject ◽  
Physical Beauty

Violence has been a part of daily life in both traditional and digital media. Consequently, neither the existence of violence in the media nor the debates on this subject are new. On the other hand, the presentation of violence in fictional content should be viewed from a different point of view, especially in the context of aesthetization. Within this context, in this chapter, the serial of Penny Dreadful is analyzed. As analyzing method, Tahsin Yücel's model of the “space/time coordinates of narrative” is used. And the subject of “aestheticization of violence” is analyzed through a serial with the elements of person, space, and time. Thus, the role of not only physical beauty but also different components in the aestheticization of violence is examined.

scholarly journals The Draupner Event: The Large Wave and the Emerging View

2017 ◽  
Vol 98 (4) ◽  
pp. 729-735 ◽  
Author(s):  
L. Cavaleri ◽  
A. Benetazzo ◽  
F. Barbariol ◽  
J.-R. Bidlot ◽  
P. A. E. M. Janssen
Keyword(s):  
Relevant Information ◽  
Space Time ◽  
Point Of View ◽  
Extreme Waves ◽  
Sea State ◽  
Wave Groups ◽  
Large Wave ◽  
Open Sea ◽  
Improved Model ◽  
2D Space

Abstract In a parallel paper mainly focused on the meteorological and oceanographic aspects, the conditions were described for the storm during which the iconic Draupner wave was recorded. Because of increased spatial resolution and improved model physics, the results provided new and previously unrecognized features of the storm, in particular of the wave spectra, features relevant for assessing the wave’s conditions nearby the Draupner platform. Starting from these, and after briefly summarizing the relevant information, the focus of this paper is on the nonlinear analysis of the local situation, with the main purpose of assessing if and how the conditions existed for the possible appearance of very large waves. An intensive analysis of the related probability is carried out, attacking the problem with two different statistical approaches, both briefly described: a completely new one working from the point of view of envelope heights, and a recent, though established, one based on space–time extreme waves. It is remarkable, and certainly supports this line of work, that the two different approaches lead independently to consistent results, supporting the idea, already derived from the meteo-oceanographic hindcast, that the wave conditions were indeed special at the position of the Draupner platform. This is related to a general analysis of high waves showing, also on the basis of 3D (2D space + time) measured wave data at open sea, how, given the severe sea state, the Draupner wave features represent what is expected at certain times and positions as the natural documented temporal evolution of wave groups.

scholarly journals On the methods of extending Dirac's equation of the electron to general relativity

1942 ◽  
Vol 7 (1) ◽  
pp. 39-50
Author(s):  
D Martin
Keyword(s):  
General Relativity ◽  
Covariant Derivative ◽  
Riemannian Geometry ◽  
Space Time ◽  
Point Of View ◽  
Dirac Equations ◽  
Usual Form ◽  
Galilean System ◽  
Second Category ◽  
Working Out

1. Introduction. The problem of extending Dirac's equation of the electron to general relativity has been attacked by many authors, by methods which fall roughly into either of two classes according as the formulation does or does not require the introduction of a local Galilean system of coordinates at each point of space-time. As examples of the former class we mention the methods of Fock (1929) and of Cartan (1938), and as representing the latter class the method described by Ruse (1937). Also, Whittaker (1937) discovered a vector whose vanishing is completely equivalent to the Dirac equations, but this method, unlike the others in the second category, does not apply the Riemannian technique to spinors but only to vectors and tensors derived from these. Now Cartan has denied the possibility of fitting a spinor into Riemannian Geometry if his point of view of spinors is adhered to, and this he argues accounts for the “choquant” properties with which they have been endowed by the geometricians in order to enable them to write down an expression of the usual form for the covariant derivative of a spinor. Consequently, doubt has been cast on the compatibility of the various methods, so in this paper an attempt is made to clarify the matter by working out explicitly the case of the general metric by some of the more important of these methods.

scholarly journals The shape dynamics description of gravity

2015 ◽  
Vol 93 (9) ◽  
pp. 956-962 ◽  
Author(s):  
Tim Koslowski
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Small Scale ◽  
Shape Dynamics ◽  
Quantum Particles ◽  
Minkowski Space Time ◽  
Time Structures ◽  
Geometric Picture

Classical gravity can be described as a relational dynamical system without ever appealing to space–time or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the shape dynamics description of gravity can be derived is a motivation to consider shape dynamics (rather than general relativity) as the fundamental description of gravity. Adopting this point of view leads to the question: What is the role of space–time in the shape dynamics description of gravity? This question contains many aspects: Compatibility of shape dynamics with the description of gravity in terms of space–time geometry, the role of local Minkowski space, universality of space–time geometry and the nature of quantum particles, which can no longer be assumed to be irreducible representations of the Poincaré group. In this contribution I derive effective space–time structures by considering how matter fluctuations evolve along with shape dynamics. This evolution reveals an “experienced space–time geometry.” This leads (in an idealized approximation) to local Minkowski space and causal relations. The small-scale structure of the emergent geometric picture depends on the specific probes used to experience space–time, which limits the applicability of effective space–time to describe shape dynamics. I conclude with discussing the nature of quantum fluctuations (particles) in shape dynamics and how local Minkowski space–time emerges from the evolution of quantum particles.

scholarly journals Low-Rank Space-Time Decoupled Isogeometric Analysis for Parabolic Problems with Varying Coefficients

2019 ◽  
Vol 19 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Angelos Mantzaflaris ◽  
Felix Scholz ◽  
Ioannis Toulopoulos
Keyword(s):  
Isogeometric Analysis ◽  
Evolution Equations ◽  
Space Time ◽  
Point Of View ◽  
Low Rank ◽  
Parabolic Problems ◽  
Computational Point ◽  
Varying Coefficients ◽  
Analysis Scheme ◽  
Parabolic Evolution Equations

AbstractIn this paper we present a space-time isogeometric analysis scheme for the discretization of parabolic evolution equations with diffusion coefficients depending on both time and space variables. The problem is considered in a space-time cylinder in {\mathbb{R}^{d+1}}, with {d=2,3}, and is discretized using higher-order and highly-smooth spline spaces. This makes the matrix formation task very challenging from a computational point of view. We overcome this problem by introducing a low-rank decoupling of the operator into space and time components. Numerical experiments demonstrate the efficiency of this approach.

Einstein flow and cosmology

2015 ◽  
Vol 30 (18n19) ◽  
pp. 1530047 ◽  
Author(s):  
J. Kouneiher
Keyword(s):  
Space Time ◽  
Cosmological Models ◽  
Point Of View ◽  
Continuous Family ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Minkowski Metric ◽  
Global Topology ◽  
Einstein's Equation ◽  
Physical Case

The recent evolution of the observational technics and the development of new tools in cosmology and gravitation have a significant impact on the study of the cosmological models. In particular, the qualitative and numerical methods used in dynamical system and elsewhere, enable the resolution of some difficult problems and allow the analysis of different cosmological models even with a limited number of symmetries. On the other hand, following Einstein point of view the manifold [Formula: see text] and the metric should be built simultaneously when solving Einstein’s equation [Formula: see text]. From this point of view, the only kinematic condition imposed is that at each point of space–time, the tangent space is endowed with a metric (which is a Minkowski metric in the physical case of pseudo-Riemannian manifolds and an Euclidean one in the Riemannian analogous problem). Then the field [Formula: see text] describes the way these metrics depend on the point in a smooth way and the Einstein equation is the “dynamical” constraint on [Formula: see text]. So, we have to imagine an infinite continuous family of copies of the same Minkowski or Euclidean space and to find a way to sew together these infinitesimal pieces into a manifold, by respecting Einstein’s equation. Thus, Einstein field equations do not fix once and for all the global topology. [Formula: see text] Given this freedom in the topology of the space–time manifold, a question arises as to how free the choice of these topologies may be and how one may hope to determine them, which in turn is intimately related to the observational consequences of the space–time possessing nontrivial topologies. Therefore, in this paper we will use a different qualitative dynamical methods to determine the actual topology of the space–time.

HAMILTONIAN THEORY OF THE RELATIVISTIC STRING

1990 ◽  
Vol 02 (03) ◽  
pp. 355-398 ◽  
Author(s):  
G.P. Pron’ko
Keyword(s):  
String Theory ◽  
Spectral Problem ◽  
Dimensional Space ◽  
Space Time ◽  
Point Of View ◽  
Relativistic String ◽  
Hamiltonian Theory ◽  
Gauge Fixing ◽  
Dimensional Space Time ◽  
Invariant Gauge

The relativistic string theory is considered from the Hamiltonian point of view. It is proposed to formulate the dynamics of string in d-dimensional space-time with the help of the auxiliary spectral problem. This approach gives the possibility to construct a completely new set of variables of string relevant for Lorentz-invariant gauge fixing. The notion of smooth string is introduced for which the successive relativistic invariant quantization could be done explicitly for the d=4 case.

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